The relationship to the affine Springer fibers considered in this paper is as follows. The curve \(C\)  may be chosen so that the unique singularity is over \(0\in X\) . Its local form corresponds to \(\gamma =st\in \fg ()\)  as before, for \(s=(1,\rho ,\ldots ,\rho ^{n-1})\)  where \(\rho \)  is a primitive \(n\) :th root of unity. Let
\((a,0)\in ^\heartsuit \times X\) . Then [1]} says that
\(_a\times ^{P^{red}_0(J_a)} ^{\gamma }_\rightarrow \widetilde{}_a\) 
